Subseasonal variations of tropical convection and week two

prediction of wintertime western North American rainfall

Jeffrey S. Whitaker and Klaus M. Weickmann

NOAA-CIRES Climate Diagnostics Center, Boulder, Colorado

Manuscript to appear in J. Climate

Submitted to Journal of Climate

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Corresponding author address: Jeffrey S. Whitaker, NOAA-CIRES Climate

Diagnostics Center, 325 Broadway, Boulde-3328. jsw@cdc.noaa.gov

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Abstract

A statistical prediction model for weekly rainfall during winter over western North

America is developed which uses tropical outgoing longwave radiation (OLR) anomalies

as a predictor. The effects of El Nino-Southern Oscillation (ENSO) are linearly removed

from the OLR to isolate the predictive utility of subseasonal variations in tropical

convection. A single canonical correlation (CCA) mode accounts for most of the

predictable signal. The rank correlation between this mode and observed rainfall

anomalies over Southern California is 0.2 for a two-week lag, which is comparable to

correlation between a weekly ENSO index and weekly rainfall in this region. This

corresponds to a doubling of the risk of extreme rainfall in Southern California when the

projection of tropical OLR on the leading CCA mode two weeks prior is extremely large,

compared to times when it is extremely small. ‘Extreme’ is defined as being in the upper

or lower quintile of the probability distribution.

The leading CCA mode represents suppressed convection in the equatorial Indian

Ocean and enhanced convection just south of the equator east of the dateline. OLR

regressed on the time series of this mode show an eastward progression of the suppressed

region to just south of the Philippines at the time of maximum California rainfall

enhancement. The region of enhanced convection east of the dateline remains quasi-

stationary. Associated with this tropical OLR evolution is the development of upper

tropospheric westerly wind anomalies near 30oN in the eastern Pacific. Synoptic-scale

weather systems are steered farther east toward California by these enhanced westerlies.

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Since most operational weather prediction models do not accurately simulate

subseasonal variations in tropical convection, statistical prediction models such as the one

presented here may prove useful in augmenting numerical predictions. An analysis of four

years of operational week two ensemble predictions indicates that the level of skill

provided by the statistical model is comparable to that of the operational ensemble mean.

Since by week two the operational forecast model has lost its ability to represent

convectively coupled circulation associated with the subseasonal tropical convective

variability, the statistical model provides essentially independent information for the

forecaster.

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1. Introduction.

Variations of tropical convection on subseasonal time-scales are known to affect

the distribution of precipitation over western North America in wintertime (Mo and

Higgins 1998a,b, Jones 2000). However, many, if not all, current operational weather

prediction models are unable to predict subseasonal variations of tropical convection,

particularly those associated with the Madden-Julian oscillation (MJO), at ranges beyond a

few days (Hendon at al, 2000). In fact, current data assimilation systems do not even

capture aspects of the MJO very well, most likely because it occurs in a region of sparse

observations where the analysis is heavily influenced by the assimilating model (Newman

et al 2000). This suggests that precipitation forecasts over North America could be

improved, particularly in the medium and extended range, by improving predictions of

subseasonal variations in tropical convection.

Waliser et al (1999) developed a statistical model to predict tropical rainfall

variability at lead times of 5-20 days and found that the statistical model performed

considerably better than global numerical forecasts from the National Centers for

Environmental Prediction (NCEP). However, since their model used bandpass filtered

OLR as a predictor, it cannot easily be used to make real-time predictions. In this study,

we will present a statistical prediction model utilizing the latest 7-day average tropical

OLR field to predict rainfall over western North America directly two weeks later. The

model has been designed to be used as a real-time forecast model, and to isolate the

predictability of western North American rainfall associated with subseasonal tropical

convective variability. Since the value of El Nino/Southern Oscillation (ENSO) in

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predicting seasonal mean rainfall in this region has already been well established (Schonher

and Nicholson 1989, Barnston et al 1999), we chose to focus on the predictability

associated with subseasonal OLR variability by linearly removing the ENSO signal from

the weekly OLR data. The predictive skill obtained by using subseasonal OLR as a

predictor is compared with week two rainfall predictions produced by the NCEP

operational ensemble prediction system (Toth and Kalnay 1993) and the predictability of

weekly rainfall associated with ENSO. Since our model is linear, and only takes into

account the initial distribution of tropical OLR, it can be considered a lower bound on the

potential for increasing forecast skill by improving the representation of subseasonal

tropical convective variability in operational prediction systems.

2. Data and Analysis Procedure.

The 2.5o gridded daily OLR dataset described by Liebmann and Smith (1996) is

used as a proxy for tropical convection. Data for 25 winter seasons is used, from

December – February (DJF) 1974/1975 to 1999/2000. DJF 1978/1979 is excluded, since

much of the data is missing due to instrument problems. The data is smoothed to

emphasize large-scale features using a Gaussian spectral filter (Sardeshmukh and Hoskins

1984) of the form exp(-(n/20)2), where n is the total wavenumber in spherical harmonic

space. This is roughly equivalent to averaging the OLR over a circular region with a

radius of about 800 km. After the spatial smoothing, the OLR data is interpolated to a 5o

grid and then temporally smoothed by applying a seven-day running average. The linear

ENSO signal in OLR is defined by linearly regressing the spatially smoothed, weekly OLR

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data on to the first two principal components (PCs) of 7-day averaged sea surface

temperature from the NCEP/NCAR reanalysis (Kalnay et al, 1996)1. This linear signal is

removed from the data in order to isolate the predictability associated with subseasonal

tropical convective variations. This is typically done by band-pass filtering the data (as in

Waliser et al 1999), but for real-time predictions band-pass filtering is problematic. Figure

1 shows the standard deviation of the smoothed weekly OLR field (with ENSO removed)

from 30oN – 30oS, along with the analysis domain used (15oN – 25oS, 45oE – 80oW).

Precipitation from the reanalysis dataset is used as a predictand. Reanalysis

precipitation is an average of the first six hours of a forecast and thus is subject to

limitations and biases of the assimilating model (Kalnay et al, 1996). However, for

wintertime conditions in which most of the precipitation is due to condensation in large-

scale, dynamically forced ascent, the reanalysis precipitation field is less likely to reflect

model errors then it is in summertime, when the precipitation is convective and driven

more by local conditions. We chose to use reanalysis precipitation because it is available

globally, and we had no a priori knowledge that the predictable signal associated with

subseasonal variations in tropical convection would be located in regions where

precipitation is directly measured. Since it turned out that the largest predictable signal

occurs in California, we have redone a portion of the analysis with gauge data in that

region (see section 5). A weak Gaussian spectral filter is applied to precipitation, of the

same form as described above, but with an e-folding distance of 60 in wavenumber space.

This is done to remove spurious precipitation in the analysis associated with the spectral

1 The four times daily SST in the reanalysis is interpolated from a daily analysis after 1981, prior to 1981 it is interpolated from a monthlyanalysis. However, the first two EOFs are strongly related to ENSO and thus have very long decorrelation time scales (much longer thana month), so this difference is not likely to be important.

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truncation of specific humidity, particularly in the vicinity of steep topography. Figure 2

shows the standard deviation of DJF weekly reanalysis precipitation and the analysis

domain (100oW – 160oW, 25oN – 65oN)

Canonical correlation analysis (CCA) is a technique that isolates the linear

combination of data from a predictor field and the linear combination of data from a

predictand field that have the maximum correlation coefficient. If all of the CCA vectors

are used to make a forecast, the result is identical to a multiple linear regression forecast.

The decomposition of the regression matrix into modes that maximize the correlation

between the predictor and predictand distinguishes CCA from multiple linear regression.

To avoid problems that arise because the number of observation times is less than the

number of grid points in the spatial fields, the analysis is performed in the truncated

principal component (PC) space of the two fields (Barnett and Preisendorfer, 1987).

Computation of the canonical vectors then amounts to performing a singular value

decomposition (SVD) of the covariance matrix between the normalized PCs of the

predictor and predictand fields (Bretherton et al, 1992). The singular values are the

canonical correlations. For most of the results presented here, the first 20 PCs were

retained for both the predictor and predictand fields.

CCA is designed to work for fields whose probability distribution function (PDF)

is Gaussian. Weekly precipitation can be significantly non-Gaussian, particularly in dry

regions. Weekly tropical OLR also can be significantly non-Gaussian in descending

regions, but in the subspace spanned by the leading EOFs OLR is fairly Gaussian (Winkler

et al, 2000). To ensure that the skewness of the weekly precipitation PDF is not affecting

the analysis, we have used the probability-integral transform described by Sardeshmukh et

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al (2000) to convert weekly precipitation into a Gaussian variable with zero mean and the

same standard deviation shown in Fig. 2.

To summarize, prior to computing the EOFs, tropical OLR is smoothed using a

Gaussian spectral filter, 7-day averages are taken, the linear ENSO signal is removed, and

the daily climatology of the resulting quantity is removed. Precipitation is spectrally

smoothed, 7-day averages are computed, and the resulting data is transformed into a

Gaussian quantity having the same variance. The daily climatology of this quantity is then

removed. An EOF analysis is then performed, and a CCA is done in the PC space spanned

by the first 20 modes of each variable. Truncations of 5, 10 15 and 25 were also tried.

Keeping more modes improves forecasts up to 20, but beyond that sampling error begins

to degrade forecasts. Cross-validation or “jackknifing” (Barnett and Preisendorfer 1987)

is used to assess the skill of the statistical model, so that for each of the 25 winter seasons

only data from the other 24 winter seasons is used to construct the model. Statistical

significance is assessed using a Monte-Carlo technique (Wilks, 1995) which assumes that

data is not serially correlated from one year to the next.

3. Forecast skill.

Figure 3 shows the Spearman rank-order correlation (Press et al 1989) between

the leading canonical predictor variable (a time series obtained by projecting the initial

OLR data on the leading canonical predictor vector) and analyzed precipitation two weeks

later, at each grid point for 25 winters of forecasts. Since this map shows the correlation

of an index of tropical convective activity and analyzed precipitation, as opposed to the

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correlation between forecast and analyzed precipitation, both positive and negative values

indicate skill. A map of the correlation between precipitation forecast using the leading

canonical vector and analyzed precipitation two weeks later looks like the absolute value

of the quantity plotted in Fig. 3. The predictable signal associated with this vector

consists of a dipolar pattern with opposite signed precipitation anomalies in California and

British Columbia. The strongest predictable signal occurs off the coast of California,

where correlations exceed 0.2. Forecast skill does not improve significantly by including

more vectors, indicating that most of the predictable signal is captured by the leading

vector.

In order to illustrate the potential utility of these forecasts, we have calculated the

conditional probability of above normal precipitation associated with extreme values in the

leading canonical variable. As discussed by Madden (1989), even a low correlation

between predictor and predictand time series can allow for skillful prediction of shifts in

the probability of extremes in the predictand. Here we define “above normal” to be in the

upper tercile of the distribution, and “extreme” to be in the upper quintile of the

distribution. This enables us to quantify how the occurrence of extreme values of the

leading canonical predictor variable alters the risk of anomalously wet conditions over

Western North America two weeks later. The results of these calculations are

summarized by the ratio of the probability of above normal precipitation to the

climatological probability (33%) when the leading canonical variable two weeks prior is in

the upper or lower quintile of its distribution (Figure 4). Similar calculations were

performed for seasonal temperature extremes associated with ENSO by Wolter et al

(1999). Figure 4 shows that although the rank correlation between the leading canonical

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variable and precipitation two weeks later is modest (0.2), the risk of above normal rainfall

off the coast of California is increased by up to 50% two weeks after extremely large

values of the leading canonical predictor variable are observed. Conversely, the risk of

below normal rainfall is reduced by 50-60%. Risk ratios of about the same magnitude,

but in the opposite sense, are found along the coast of British Columbia and in the Gulf of

Alaska.

Another way to gauge the potential utility of subseasonal tropical OLR variability

as a forecast tool is to compare it to other well-known predictors of precipitation over

Western North America. ENSO is known to have a large impact on the probability

distribution of seasonal mean precipitation in this region. Figure 5 quantifies its effect on

the weekly precipitation distribution. The rank correlation between a weekly ENSO index

(the first PC of tropical SST) and precipitation two weeks later is similar to that shown in

Figure 3 in the California region. This indicates that subseasonal variations of tropical

convection have at least as large an impact on the probability distribution of weekly

precipitation in this region as does ENSO. Barsugli et al (1999) showed that ENSO had a

very large positive impact on extended range operational ensemble forecasts of 500 hPa

height in the Pacific-North American region during the winter of 1997/98. It is reasonable

to expect that the impact of subseasonal tropical OLR variations on operational forecasts

could just as large, at least in those cases where the projection of tropical OLR on the

leading canonical vector is very high.

We have also directly compared gridded ensemble mean week two precipitation

forecasts from the operational NCEP ensemble prediction system (Toth and Kalnay, 1993)

to our CCA forecasts, for four winters (1996/1997 – 1999/2000). The rank correlation

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between forecast and analyzed precipitation for the operational NCEP ensemble is shown

in Figure 6a. The rank correlation between the leading canonical variable and analyzed

precipitation for the same four-winter period is shown in Fig. 6b. This map differs from

Fig. 3 only because of the shorter time period used to calculate the correlation. Because

Fig. 6a shows the correlation between forecast and analyzed precipitation, while Fig. 6b

shows the correlation of an index with analyzed precipitation, only positive values indicate

skill in Fig. 6a, while both positive and negative values may indicate skill in Fig. 6b. The

ensemble mean forecast has significant skill all along the West Coast, with correlations

exceeding 0.4 in California for the four-winter period. The CCA forecast, using only the

first canonical variable, has roughly the same level of skill along the West Coast for this

four-winter period (Figure 6b). These forecasts contain essentially independent

information, since the current operational models have little skill in predicting subseasonal

variations in tropical convection at this forecast range (Hendon et al 2000, Waliser et al

2000). This is supported by the fact that the correlation between the CCA and ensemble

mean forecasts along the West Coast is not significantly different than zero at the 95%

level (not shown). Therefore, there is a significant potential for improving extended range

precipitation forecasts along the West Coast by either; 1) improving the representation of

subseasonal tropical convective variability in forecast models, or 2) blending the essentially

independent information contained in statistical and numerical forecasts.

4. Diagnosis of the leading canonical vector.

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Most of the predictable signal in West Coast precipitation comes from the leading

pair of canonical vectors. In this section, we investigate the large-scale circulation and

OLR fields associated with this pattern.

The structure of the leading canonical predictor vector is shown in Fig. 7.

Enhanced convection just south of the equator and east of the dateline, with suppressed

convection in the equatorial Indian Ocean is associated with an increased (decreased)

probability of above (below) normal rainfall in California (British Columbia) two weeks

later (Figure 3).

The evolution of the 7-day running mean OLR field associated with the leading

canonical predictor variable (CPV), as defined by lag-regression, is shown in Fig. 8. A

flare-up of convection east of the dateline, in the vicinity of the South Pacific Convergence

Zone (SPCZ) is the primary feature associated with positive values of the CPV, along with

a suppression of convection in the eastern equatorial Indian Ocean. The region of

suppressed convection propagates eastward over the next two weeks, while the region of

enhanced convection remains quasi-stationary and decays. The negative OLR anomaly

over California at the verification time (Fig. 8c) is consistent with increased probability of

rainfall in that region at two-week lag (Fig. 3).

Lag-regression of the CPV on 7-day running mean 200 hPa streamfunction is used

to illustrate the evolution of the large-scale low frequency circulation field (Fig. 9). An

upper tropospheric cyclone, with associated tropical westerly wind anomalies propagates

eastward out of the Indian Ocean along with the suppressed convection. An upper

tropospheric cyclone in the Eastern Pacific develops after the flare-up of convection east

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of the dateline. This trough strengthens and moves slightly eastward between days 0 and

14.

The growth of anomalous upper-tropospheric westerlies in the Eastern Pacific

occurs simultaneously with the onset of precipitation in California. We hypothesize that

the mechanism for California rainfall enhancement is related to the steering effect of these

westerlies on synoptic-scale weather systems in the Eastern Pacific. To illustrate this, we

have used 7-day running mean high-pass filtered 850 hPa meridional wind variance as a

proxy for synoptic-eddy activity. The high-pass filter used is simply the deviation of daily

averages from five-day running means. Lag-regression maps (Fig. 10) show that there is a

significant enhancement of synoptic-eddy activity off the coast of California in the two

weeks after a positive projection of tropical OLR on the leading canonical predictor

vector. We hypothesize that the development of the OLR anomalies associated with the

CPV (Figure 8a) force upper-tropospheric westerly wind anomalies in the far eastern

Pacific. These westerly wind anomalies act to steer weather systems farther east than

usual, allowing them to reach the California coast rather than occluding and decaying in

the Gulf of Alaska. The fact that both the tropical OLR anomalies and the associated

upper tropospheric westerlies are fairly persistent once established leads to the

predictability of California rainfall in the two week range shown in Fig. 3.

The OLR field associated with the CPV (Fig. 8) is fairly complicated. From a

monitoring perspective, it would be useful to know which features are primarily

responsible for the upper tropospheric wind signal in the Eastern Pacific. Fig. 8a shows

that during times when there is a positive projection on the leading canonical predictor

vector there are typically two opposite signed OLR anomalies, one located in the

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equatorial Indian Ocean and one near 5oS east of the dateline. Here we use two indices

that measure the strength of tropical convection in these two regions to identify the

extratropical circulation features associated with each separately. The goal is to

understand the relative roles of convection in these two regions in producing the

California rain signal two weeks later. The indices we use are based on a rotated EOF

analysis of the OLR data. As a measure of the Indian Ocean convection we use the

expansion coefficient for rotated EOF 2, and for the eastern Pacific convection we use a

linear combination of the expansion coefficients of rotated EOFs 5 and 9 (not shown).

The OLR field regressed on these two indices (Fig. 11) shows that they indeed do capture

the essential aspects of the OLR field typically associated with the CPV. The 200 hPa

streamfunction field regressed on these two indices at two week lag (Fig. 12) show that,

although both the Indian Ocean and eastern Pacific convective anomalies are associated

with enhanced upper level westerlies off the coast of California two weeks later, enhanced

convection in eastern Pacific is contributing much more to the total westerly wind signal

associated with the CPV (Fig. 9c) than suppressed convection in the Indian Ocean.

Therefore, we conclude that it is enhanced convection east of the dateline near 5oS that is

the primary feature associated with the CPV that is responsible for the precipitation signal

in California two weeks later. These results are in qualitative agreement with previous

studies of the linear, steady state response to idealized tropical heating distributions (such

as Ting and Yu, 1998), although there are significant differences in detail. For example,

the upper tropospheric westerly wind signal off the coast of California is considerably

farther east than linear, steady state dynamics would predict. This is likely due to

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processes typically not represented in linear models, such as transient-eddy feedback, and

to the restrictions imposed by the steady-state assumption.

5. Results with California rain-gauge data.

All of the results presented so far have used reanalysis precipitation as the

predictand. As discussed in section 2, reanalysis precipitation is not directly constrained

by observations, and therefore is subject to the limitations and biases of the assimilating

model. In this section we present results with daily California precipitation gauge data as

a predictand. We choose California because the results with reanalysis precipitation

suggest that it is the region with the strongest predictable signal where gauge data is

available.

Weekly California precipitation station data for the 24 winters between 1974/75

and 1998/99 (excluding 1978/79) is used. The data is derived from the daily precipitation

dataset described by Eischeid et al (2000). 442 stations are available in California for this

time period. As a predictand we use an average of all the stations in the Central and

Southern Coast drainage climate divisions. The results are not significantly different if

either of the two climate divisions is used alone, or if a multivariate analysis is performed

using all California climate divisions. As before, a probability-integral transform is applied,

and the daily climatology is removed. This yields an index of coastal California

precipitation which is Gaussian distributed. Since the predictand is now a scalar, the CCA

reduces to finding a vector representing the covariance between the leading 20 normalized

PCs of tropical OLR and the normalized coastal California precipitation index two weeks

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later. The predictor index is then simply the projection of the observed OLR PCs on to

this vector. Cross-validation is used so that for a given winter season, only data from the

other 23 winters is used to compute the covariance vector.

The rank-order correlation between the OLR predictor index and the coastal

California precipitation index two weeks later is 0.2, which is comparable to that obtained

with reanalysis precipitation (Fig. 3). Lag-regression of the 7-day running mean tropical

OLR on to the OLR predictor index (not shown) yields an evolution very similar to that

associated with the leading canonical predictor variable for reanalysis precipitation (Fig.

8). This indicates that reanalysis, at least in winter, does provide a reasonable estimate of

precipitation variability in this region on weekly timescales. Fig. 13a shows the changes

in the probability of above, below and near normal coastal California precipitation

associated with extreme values of the predictor index. The risk of above normal weekly

rainfall in coastal California is increased by 33%, relative to the climatological probability,

when the OLR predictor index is in the upper quintile. Conversely, the risk of below

normal precipitation is reduced by 66%. Similar results are obtained for below normal

rainfall when the predictor is in the lower quintile. These results are very similar to that

obtained for reanalysis precipitation in the California region (Fig. 4). Therefore, we

conclude that the results presented here with reanalysis estimated precipitation provide a

realistic estimate of the week two predictability of actual rainfall along the West Coast of

North America associated with subseasonal tropical OLR variations.

6. Summary and conclusions.

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Subseasonal variations of tropical convection can be used to improve the skill of

two-week precipitation forecasts over western North America, and particularly in

California. The level of skill obtained from a simple linear statistical model is comparable

to that provided by current numerical forecasts (which do not accurately simulate

subseasonal tropical convective variability). Using a weekly ENSO index as a predictor of

California precipitation two weeks later also yields a similar level of skill. However, since

the effect of ENSO on tropical convection is fairly well represented in numerical weather

prediction models (Barsugli et al 1999), a weekly ENSO index does not yield additional

predictive information. Most of the results presented here utilize reanalysis precipitation

as a predictand, although similar levels of skill were shown using California rain-gauge

data.

The dynamical mechanism associated with this predictability is primarily related to

the remote forcing of upper tropospheric westerly wind anomalies just off the coast of

California by enhanced tropical convection just south of the equator and east of the

dateline. Synoptic-scale weather systems which would otherwise occlude and decay in the

Gulf of Alaska are steered farther east toward the California coast by these enhanced

westerlies. Anomalous tropical convection in the eastern equatorial Indian Ocean also

plays a similar role in the prediction of California rainfall, although its impact on upper

tropospheric westerlies in the Eastern Pacific is much weaker.

Higgins et al. (2000) have examined the relationship between extreme three-day

precipitation totals along the West Coast of the United States and concurrent intraseasonal

tropical OLR patterns. They found that extreme precipitation events in Southern

California tend to be associated with enhanced tropical convection between 150oE and the

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dateline, and suppressed convection just east of the dateline. This is quite different that

the pattern of tropical OLR which we find is associated with the highest predictability of

California rainfall two weeks later. We attribute this difference to the fact that our

analysis is designed to pick out patterns of OLR and West Coast precipitation that have

the highest correlation at two week lag, while the compositing used by Higgins et al

(2000) will reveal the pattern of OLR that tends to occur simultaneously with heavy

precipitation along the West Coast. These patterns need not be the same, and the fact

that they are not implies that the precipitation events in the Higgins et al (2000) composite

are not predictable two weeks in advance using tropical OLR information alone.

Jones (2000) has examined the relationship between the Madden-Julian (MJO)

oscillation (as defined by the leading two EOFS of 20-90 day bandpass filtered OLR) and

the frequency of extreme rainfall events in California. He found an increased frequency of

extreme events when the MJO was active. Our analysis uses the first 20 PCs of tropical

OLR, and therefore includes more than just the MJO. In fact, the leading canonical

predictor vector does not project very strongly on the first two EOFs of OLR, more than

10 EOFs are needed to represent its structure. In order to assess the relative importance

of the MJO, as opposed to other modes of subseasonal tropical convective variability, we

have redone the CCA using only the first two PCs of OLR. Fig. 14 shows the rank-order

correlation between the resulting leading canonical variable (which is primarily the leading

OLR PC) and the reanalysis precipitation two weeks later. Comparing with Fig. 3, it is

evident that the region of maximum predictability associated with the MJO is located over

the southwest U.S., instead of off the coast of California. When viewed as a domain

average, the predictability associated with the MJO is a relatively small portion of the total

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predictability associated with subseasonal tropical convective variability. However, locally

in southern California and the southwest U.S., the MJO appears to be producing most of

the predictable precipitation signal. Therefore, we conclude that although the MJO may

be a useful predictor of rainfall in southern California and the desert Southwest, there are

other important aspects of subseasonal tropical convective variability that should be taken

into account when making predictions over a larger area.

In this study we have shown that subseasonal tropical convective activity is linearly

related to rainfall near the West Coast of North America two weeks later, and that this

linear relationship can be used to improve precipitation predictions. However, we have

not proven that the predictability is ultimately rooted in tropical processes, since the

possibility remains that the OLR anomalies shown in Fig. 8a are being forced by

circulation features of mid-latitude origin. To examine this question, we have produced

CCA forecasts using streamfunction at 250 and 850 hPa, in the region 15-70oN and 60oE

to 120oW, as a predictor. The computational procedure is the same as outlined in section

2, but instead of using 20 EOFs of tropical OLR as predictors, we use the first 20 EOFs of

the combined vector of 250 and 850 hPa streamfunction (with ENSO linearly removed).

Fig 15 shows the rank correlation between week two forecast (using all 20 canonical

predictor vectors) and analyzed reanalysis precipitation, using tropical OLR as a predictor

(Fig 15a), Northern Hemisphere extratropical streamfunction as a predictor (Fig. 15b),

and extratropical streamfunction with the tropical OLR signal (as defined by the first 20

EOFs) linearly removed (Fig. 15c). Comparing Fig. 15a with Fig 15b, it is clear that a

large part of the predictable precipitation signal along the West Coast cannot be captured

using the extratropical circulation alone. Furthermore, Fig. 15c shows there is virtually no

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predictive utility in that part of the circulation that is independent of tropical OLR, at least

along the West Coast. Although we have not addressed the ultimate origin of the tropical

OLR patterns shown in Fig. 8, if they were primarily forced by mid-latitude circulation

anomalies, we would have expected forecasts of West Coast precipitation using mid-

latitude circulation as a predictor to be at least as skillful as those using tropical OLR.

These results suggest that most of the predictable signal in West Coast precipitation is

related to tropical processes at two week lag. Although the mid-latitude circulation alone

can be used to make skillful forecasts, most of the skill comes from that part of the

circulation that is linearly related to (and most likely forced by) tropical convective

processes.

The statistical model used here is linear, and does not use any mid-latitude

circulation information. Presumably, the remote impacts of tropical convection may be

affected by mid-latitude flow conditions, particularly in the vicinity of the Pacific Jet.

Numerical weather prediction models, if they were able to accurately simulate subseasonal

tropical convective variability, could conceivably exploit such nonlinear tropical-

extratropical interactions. Therefore, the skill of statistical predictions presented here

may be considered a lower bound on the potential for improved predictability of West

Coast rainfall in the week two range. Until numerical models can better simulate tropical

variability on subseasonal timescales, they should be augmented with statistical models,

which provide essentially independent information associated with the state of tropical

convection at the initial time. Exactly how to combine the output of statistical and

numerical models to exploit the predictive information inherent in satellite measurements

of tropical convection is an active area of research.

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Acknowledgements: Support for this research was provided by the U.S. CLIVAR

PanAmerican Climate Studies program (PACS). We thank Dr. Matthew Newman for

helpful discussions on the finer points of linear regression and SVD, and two anonymous

reviewers for insightful comments.

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Figure Captions:

Figure 1: Standard deviation of 7-day averaged, spectrally smoothed OLR with ENSO

linearly removed. Contour interval is 2 Wm-2. Values greater than 14 Wm-2 are shaded.

The boxed region is the domain used for the CCA.

Figure 2: Standard deviation of weekly, spectrally smoothed precipitation from

reanalysis. Contour interval is 2 mm. Values greater than 21 mm are shaded. The boxed

region is the domain used for the CCA.

Figure 3: The rank-order correlation between the leading canonical predictor variable

(computed using the leading 20 PCs of tropical OLR) and the analyzed precipitation two

weeks later. Positive contours are thicker, the zero line is omitted and shading indicates

statistical significance.

Figure 4: Risk (relative to climatological risk of 33%) of precipitation being in the upper

tercile given that the leading canonical predictor variable two weeks prior is in the upper

(A) or lower (B) quintile. Shaded areas are significantly different than 1.0 at the 95%

level, thicker contours are greater than 1.0. Contour interval is 0.1, and only contours less

than 0.9 and greater than 1.1 are plotted.

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Figure 5: The rank-order correlation between a weekly ENSO index (the leading PC of

tropical SST) and analyzed precipitation two weeks later. Positive contours are thicker,

the zero line is omitted, and shading indicates statistical significance.

Figure 6: (A) rank-order correlation between analyzed and operational ensemble mean

week two forecast precipitation for four winters (1996/1997 - 1999/2000). (B) rank-order

correlation between analyzed precipitation and leading canonical predictor variable two

weeks prior for same time period (which is different than the time period used to compute

Fig. 3). Positive contours are thicker, the zero line is omitted, and shading indicates

statistical significance.

Figure 7: Map of leading canonical predictor vector, representing tropical OLR. Positive

contours are thicker, and the zero line is omitted.

Figure 8: OLR regressed on leading canonical predictor variable at lag 0 (A), 7 (B) and

14 (C) days. Maps are scaled for one standard deviation of the canonical predictor

variable. Contour interval is 1.5 Wm-2. Positive contours are thicker, the zero line is

omitted and shading indicates statistical significance. Day 0 is the initial time for CCA

forecasts, and day 14 is the forecast verification time.

Figure 9: As in Figure 8, but for 200 hPa streamfunction. Contour interval is 5 x 106

m2s-1 Contour levels greater than or equal to zero are thicker, and shading indicates

statistical significance.

24

Figure 10: As in Figure 8, but for 850mb high-pass meridional wind variance. Contour

interval is 1 m2s-2. Positive contours are thicker, the zero line is omitted, and shading

indicates statistical significance.

Figure 11: OLR regressed on indices of Indian Ocean (A) and eastern Pacific (B)

convection. Contour interval 1.5 Wm-2. Positive contours are thicker, the zero line is

omitted, and shading indicates statistical significance.

Figure 12: 200 hPa streamfunction regressed on indices of Indian Ocean (top panel) and

eastern Pacific (bottom panel) convection at two-week lag. Contour interval 5 x 106 m2s-

1. Contour levels greater than or equal to zero are thicker, and shading indicates statistical

significance.

Figure 13: (A) Conditional tercile probabilities for observed coastal California weekly

precipitation when the OLR predictor index two weeks prior is in the upper and lower

quintiles of its distribution. The OLR predictor is constructed as described in section 5,

using the first 20 EOFs of tropical weekly OLR (with ENSO linear removed). (B)

Conditional tercile probabilities for a persistence forecast (where the predictor is the

observed weekly California rainfall two weeks prior).

Figure 14: As in Fig. 3, but for a canonical predictor variable computed using only the

leading two PCs of tropical OLR.

25

Figure 15: The rank-order correlation between week two forecast (using the first 20

leading canonical predictor vectors) and analyzed reanalysis precipitation. The predictors

used in the CCA were (A) the first 20 EOFs of tropical OLR, (B) the first 20 EOFs of

combined 250 and 850 hPa streamfunction in the region 15-70oN, 60oE-120oW, and (C)

the first 20 EOFs of 250 and 850 hPa streamfunction with that part linearly related to the

first 20 EOFs of tropical OLR removed. Contour interval is 0.05, statistically significant

positive correlations are shaded.

26

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Mo, K. C., and R. W. Higgins, 1998b: Tropical convection and precipitation regimes in

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30

Figure 1: Standard deviation of 7-day averaged, spectrally smoothed OLR with ENSOlinearly removed. Contour interval is 2 Wm-2. Values greater than 14 Wm-2 are shaded.The boxed region is the domain used for the CCA.

31

Figure 2: Standard deviation of weekly, spectrally smoothed precipitation fromreanalysis. Contour interval is 2 mm. Values greater than 21 mm are shaded. The boxedregion is the domain used for the CCA.

32

Figure 3: The rank-order correlation between the leading canonical predictor variable(computed using the leading 20 PCs of tropical OLR) and the analyzed precipitation twoweeks later. Positive contours are thicker, the zero line is omitted and shading indicatesstatistical significance.

33

Figure 4: Risk (relative to climatological risk of 33%) of precipitation being in the uppertercile given that the leading canonical predictor variable two weeks prior is in the upper(A) or lower (B) quintile. Shaded areas are significantly different than 1.0 at the 95%level, thicker contours are greater than 1.0. Contour interval is 0.1, and only contours lessthan 0.9 and greater than 1.1 are plotted.

34

Figure 5: The rank-order correlation between a weekly ENSO index (the leading PC oftropical SST) and analyzed precipitation two weeks later. Positive contours are thicker,the zero line is omitted, and shading indicates statistical significance.

35

Figure 6: (A) rank-order correlation between analyzed and operational ensemble meanweek two forecast precipitation for four winters (1996/1997 - 1999/2000). (B) rank-ordercorrelation between analyzed precipitation and leading canonical predictor variable twoweeks prior for the same time period. Positive contours are thicker, the zero line isomitted, and shading indicates statistical significance.

36

Figure 7: Map of leading canonical predictor vector, representing tropical OLR. Positivecontours are thicker, and the zero line is omitted.

37

Figure 8: OLR regressed on leading canonical predictor variable at lag 0 (A), 7 (B) and14 (C) days. Maps are scaled for one standard deviation of the canonical predictorvariable. Contour interval is 1.5 Wm-2. Positive contours are thicker, the zero line isomitted and shading indicates statistical significance. Day 0 is the initial time for CCAforecasts, and day 14 is the forecast verification time.

38

Figure 9: As in Figure 8, but for 200mb streamfunction. Contour interval is 5 x 106 m2s-1

Contour levels greater than or equal to zero are thicker, and shading indicates statisticalsignificance.

39

Figure 10: As in Figure 8, but for 850mb high-pass meridional wind variance. Contourinterval is 1 m2s-2. Positive contours are thicker, the zero line is omitted, and shadingindicates statistical significance.

40

Figure 11: OLR regressed on indices of Indian Ocean (A) and eastern Pacific (B)convection. Contour interval 1.5 Wm-2. Positive contours are thicker, the zero line isomitted, and shading indicates statistical significance.

41

Figure 12: 200 hPa streamfunction regressed on indices of Indian Ocean (top panel) andeastern Pacific (bottom panel) convection at two-week lag. Contour interval 5 x 106 m2s-

1. Contour levels greater than or equal to zero are thicker, and shading indicates statisticalsignificance.

42

0

10

20

30

40

50

predictor in lower quintilepredictor in upper quintile

prob

abili

ty

precip categorybelow normal near normal above normal

(A) CCA Forecast

0

10

20

30

40

50

predictor in lower quintilepredictor in upper quintile

precip category

below normal near normal above normal

(B) Persistence Forecast

prob

abili

ty

Figure 13: (A) Conditional tercile probabilities for observed coastal California weeklyprecipitation when the OLR predictor index two weeks prior is in the upper and lowerquintiles of its distribution. The OLR predictor is constructed as described in section 5,using the first 20 EOFs of tropical weekly OLR (with ENSO linear removed). (B)Conditional tercile probabilities for a persistence forecast (where the predictor is theobserved weekly California rainfall two weeks prior).

43

Figure 14: As in Fig. 3, but for a canonical predictor variable computed using only theleading two PCs of tropical OLR.

44

Figure 15: The rank-order correlation between week two forecast (using the first 20leading canonical predictor vectors) and analyzed reanalysis precipitation. The predictorsused in the CCA were (A) the first 20 EOFs of tropical OLR, (B) the first 20 EOFs ofcombined 250 and 850 hPa streamfunction in the region 15-70oN, 60oE-120oW, and (C)the first 20 EOFs of 250 and 850 hPa streamfunction with that part linearly related to thefirst 20 EOFs of tropical OLR removed. Contour interval is 0.05, statistically significantpositive correlations are shaded.